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Sergeu [11.5K]
2 years ago
8

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d

istribution of the number of daily requests is bell-shaped and has a mean of 61 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 61 and 94?
Mathematics
1 answer:
zaharov [31]2 years ago
5 0

Answer:

P(61≤ X≤94) = 49.85%

Step-by-step explanation:

From the given information:

The mean of the bell shaped fluorescent light bulb μ = 61

The standard deviation σ = 11

The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)

Using the empirical (68-95-99.7)rule ;

At 68% , the data lies between  μ - σ and μ + σ

i.e

61 - 11 and 61 + 11

50 and 72

At  95%, the data lies between  μ - 2σ and μ + 2σ

i.e

61 - 2(11) and 61 + 2(11)

61 - 22 and 61 +22

39   and   83

At 99.7%, the data lies between  μ - 3σ and μ + 3σ

i.e

61 - 3(11) and 61 + 3(11)

61 - 33 and 61 + 33

28   and   94

the probability equivalent to 94 is when  P(28≤ X≤94) =99.7%

This implies that ,

P(28≤ X≤94) + P(61≤ X≤94) = 99.7%

P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %    

This is so because the distribution is symmetric about the mean

P(61≤ X≤94) = 99.7 %/2

P(61≤ X≤94) = 49.85%

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Answer: 284 boxes in the shape of the cubes can be fitted in the truck.

Step-by-step explanation:

If a truck is fitted fully with the cubes, volume of the truck will be equal to the volume of cubes to be fitted.

Dimensions of the truck given in the question,

Length = 10 feet, width = 12 feet and height = 8 feet

Since, volume of a cuboid (shape of a truck) is given by the expression,

Volume = Length × Width × Height

Therefore, volume of the truck = 10 × 12 × 8

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Volume of a cube is given by the expression,

Volume = (side)³

Therefore, volume of the cube with side length 1.5 feet will be,

Volume of a cube = (1.5)³

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Let the number of cubes fitted in the truck = x

Therefore, volume of 'x' cubes = (3.375x) feet³

Since, volume of the truck = Volume of the cubes fitted

3.375x = 960

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    Therefore, 284 boxes in the shape of the cubes can be fitted in the truck.

5 0
1 year ago
Read 2 more answers
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Nadusha1986 [10]

Answer:

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Step-by-step explanation:

6 - 2y + (-8y) + 5.1 = 0

6 + 5.1 -2y -8y = 0

Add like terms

11.1 - 10y = 0

(This is simplified, but if you want to solve for y, continue)

11.1 - 10y = 0

÷10  ÷10

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y = 1.11 because 1.11 - 1.11 is 0

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I don't what that says
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3 years ago
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